I have shower tiled with travertine and along the entire bottom a thick almost rubber-like substance is slowly leaking out. It is a grey / black color. I'm assuming it is thin set that wasn't mixed properly and never completely set up. Should I be concerned, and if so what should I do about it?
I suspect that's butyl sealant that a lazy installer used to prevent moisture from wicking up behind the tile, avoiding a trip to the hardware store. You might carefully trim it off with a razor blade and cover it with what should have been used in the first place: "tub & tile caulk".
Thinset has only two consistencies: powdery when dry and concrete-like after exposure to moisture.
Thin set that is not mixed correctly will cause the tile to lay funny. The water will evaporate once the mix sets off. If it had too much water I think your first sign would be the tile scrunching down into the hollow space below it.
If you have a Shower Door track, it could be the caulk or plumbers putty they used to seal that. Sometimes a bad batch makes into the stores and it breaks down when it is supposed to just stay pliable.